Natural maps between CAT(0) boundaries
Stephen M. Buckley, Kurt Falk
TL;DR
The paper investigates the properties of natural boundary maps in CAT(0) spaces, revealing they can fail to be injective or surjective, highlighting complexities in boundary correspondences.
Contribution
It demonstrates that natural maps between various boundaries of CAT(0) spaces can lack injectivity and surjectivity, providing new insights into boundary structures.
Findings
Maps between ideal, Gromov, and end boundaries can fail to be injective or surjective
Natural map from Gromov boundary to end boundary in CAT(-1) spaces can also fail to be injective or surjective
Highlights complexities in boundary relationships of CAT(0) and CAT(-1) spaces
Abstract
It is shown that certain natural maps between the ideal, Gromov, and end boundaries of a complete CAT(0) space can fail to be either injective or surjective. Additionally the natural map from the Gromov boundary to the end boundary of a complete CAT(-1) space can fail to be either injective or surjective.
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.
Taxonomy
TopicsGeometric and Algebraic Topology · Homotopy and Cohomology in Algebraic Topology · Commutative Algebra and Its Applications